Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$ be in $A.P.$ and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to

  • [JEE MAIN 2023]
  • A

    $220$

  • B

    $210$

  • C

    $200$

  • D

    $105$

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The following values are calculated in respect of heights and weights of the students of a section of Class $\mathrm{XI}:$

  Height Weight
Mean $162.6\,cm$ $52.36\,kg$
Variance $127.69\,c{m^2}$ $23.1361\,k{g^2}$

Can we say that the weights show greater variation than the heights?